Let a set A = A 1 ∪ A 2 ∪ … ∪ A k , where A i ∩ A j = ϕ for i ≠ j ;   1 ≤ i , j ≤ k . Define the relation R from A to A by R = { x , y : y ∈ A i if and only if x ∈ A i , 1 ≤ i ≤ k }. Then, R is:

Question

Let a set A = A 1 &#8746; A 2 &#8746; &#8230; &#8746; A k , where A i &#8745; A j = &#981; for i &#8800; j ; &#160; 1 &#8804; i , j &#8804; k . Define the relation R from A to A by R = { x , y : y &#8712; A i if and only if x &#8712; A i , 1 &#8804; i &#8804; k }. Then, R is:

Aicharya · Accepted Answer

Let A = 1 , 2 , 3 Then R = 1 , 1 , 1 , 2 , 1 , 3 2 , 1 , 2 , 2 , 2 , 3 3 , 1 , 3 , 2 3 , 3 which is an equivalence relation.

Let a set A = A 1 ∪ A 2 ∪ … ∪ A k , where A i ∩ A j = ϕ for i ≠ j ;…

Solution

Let a set A = A 1 &#8746; A 2 &#8746; &#8230; &#8746; A k , where A i &#8745; A j = &#981; for i &#8800; j ;…

Solution

Let a set A = A 1 ∪ A 2 ∪ … ∪ A k , where A i ∩ A j = ϕ for i ≠ j ;…